ss4pH: The required sample size for testing a null hyphotesis for a single proportion

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single proportion.

Usage

ss4pH(N, p, p0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

The population size.

The value of the estimated proportion.

The value to test for the single proportion.

DEFF

The design effect of the sample design. By default DEFF = 1, which corresponds to a simple random sampling design.

conf

The statistical confidence. By default conf = 0.95.

power

The statistical power. By default power = 0.80.

plot

Optionally plot the effect against the sample size.

Details

We assume that it is of interest to test the following set of hyphotesis: $$H_0: P - P_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: P - P_0 = D \neq 0 $$ Note that the minimun sample size, restricted to the predefined power $\beta$ and confidence $1-\alpha$, is defined by: $$n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}$$ Where $$S^2=p(1-p)DEFF$$

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

Examples

Run this code

# NOT RUN {
ss4pH(N = 10000, p = 0.5, p0 = 0.55)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, plot=TRUE)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, DEFF = 2, plot=TRUE)
ss4pH(N = 10000, p = 0.5, p0 = 0.55, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N <- nrow(BigLucy)
p <- prop.table(table(SPAM))[1]

# The minimum sample size for testing 
# H_0: P - P_0 = 0   vs.   H_a: P - P_0 = D = 0.1
D = 0.1 
p0 = p - D 
ss4pH(N, p, p0, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: P - P_0 = 0   vs.   H_a: P - P_0 = D = 0.02
D = 0.02
p0 = p - D 
ss4pH(N, p, p0, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)
# }